Featured Research

from universities, journals, and other organizations

Physicists eye neural fly data, find formula for Zipf's law

Date:

August 5, 2014

Source:

Emory Health Sciences

Summary:

Physicists have identified a mechanism that may help explain Zipf's law -- a unique pattern of behavior found in disparate systems, including complex biological ones. The mathematical models demonstrate how Zipf's law naturally arises when a sufficient number of units react to a hidden variable in a system.

Share This

Physicists have identified a mechanism that may help explain Zipf's law -- a unique pattern of behavior found in disparate systems, including complex biological ones. The journal Physical Review Letters is publishing their mathematical models, which demonstrate how Zipf's law naturally arises when a sufficient number of units react to a hidden variable in a system.

Related Articles

"We've discovered a method that produces Zipf's law without fine-tuning and with very few assumptions," says Ilya Nemenman, a biophysicist at Emory University and one of the authors of the research.

The paper's co-authors include biophysicists David Schwab of Princeton and Pankaj Mehta of Boston University. "I don't think any one of us would have made this insight alone," Nemenman says. "We were trying to solve an unrelated problem when we hit upon it. It was serendipity and the combination of all our varied experience and knowledge."

Their findings, verified with neural data of blowflies reacting to changes in visual signals, may have universal applications. "It's a simple mechanism," Nemenman says. "If a system has some hidden variable, and many units, such as 40 or 50 neurons, are adapted and responding to the variable, then Zipf's law will kick in."

That insight could aid in the understanding of how biological systems process stimuli. For instance, in order to pinpoint a malfunction in neural activity, it would be useful to know what data recorded from a normally functioning brain would be expected to look like. "If you observed a deviation from the Zipf's law mechanism that we've identified, that would likely be a good place to investigate," Nemenman says.

Zipf's law is a mysterious mathematical principle that was noticed as far back as the 19th century, but was named for 20th-century linguist George Zipf. He found that if you rank words in a language in order of their popularity, a strange pattern emerges: The most popular word is used twice as often as the second most popular, and three times as much as the third-ranked word, and so on. This same rank vs. frequency rule was also found to apply to many other social systems, including income distribution among individuals and the size of cities, with a few exceptions.

More recently, laboratory experiments suggest that Zipf's power-law structure also applies to a range of natural systems, from the protein sequences of immune receptors in cells to the intensity of solar flares from the sun.

"It's interesting when you see the same phenomenon in systems that are so diverse. It makes you wonder," Nemenman says.

Scientists have pondered the mystery of Zipf's law for decades. Some studies have managed to reveal how a feature of a particular system makes it Zipfian, while others have come up with broad mechanisms that generate similar power laws but need some fine-tuning to generate the exact Zipf's law.

"Our method is the only one that I know of that covers both of these areas," Nemenman says. "It's broad enough to cover many different systems and you don't have to fine tune it: It doesn't require you to set some parameters at exactly the right value."

The blowfly data came from experiments led by biophysicist Rob de Ruyter that Nemenman worked on as a graduate student. Flies were turned on a rotor as they watched the world go by, hundreds of times. The moving scenes that the flies repeatedly experienced simulated their natural flight patterns. The researchers recorded when neurons associated with vision spiked, or fired. All sets of the data largely matched within a few hundred microseconds, showing that the flies' neurons were not randomly spiking, but instead operating like precise coding machines.

If you think of a neuron firing as a "1" and a neuron not firing as a "0," then the neural activity can be thought of as words, made up of 1s and 0s. When these "words," or units, are strung together over time, they become "sentences."

The neurons are turning visual stimuli into units of information, Nemenman explains. "The data is a way for us to read the sentences the fly's vision neurons are conveying to the rest of the brain."

Nemenman and his co-authors took a fresh look at this fly data for the new paper in Physical Review Letters. "We were trying to understand if there is a relationship between ideas of universality, or criticality, in physical systems and neural examples of how animals learn," he says.

In order to navigate in flight, the flies' visual neurons adapt to changes in the visual signal, such as velocity. When the world moves faster in front of a fly, these sensitive neurons adapt and rescale. These adaptions enable the flies to adjust to new environments, just as our own eyes adapt and rescale when we move from a darkened theater to a brightly lit room.

"We showed mathematically that the system becomes Zipfian when you're recording the activity of many units, such as neurons, and all of the units are responding to the same variable," Nemenman says. "The fact that Zipf's law will occur in a system with just 40 or 50 such units shows that biological units are in some sense special -- they must be adapted to the outside world."

The researchers provide mathematical simulations to back up their theory. "Not only can we predict that Zipf's law is going to emerge in any system which consists of many units responding to variable outside signals," Nemenman says, "we can also tell you how many units you need to develop Zipf's law, given how variable the response is of a single unit."

They are now researching whether they can bring their work full circle, by showing that the mechanism they identified applies to Zipf's law in language.

"Letters and words in language are sequences that encode a description of something that is changing over time, like the plot line in a story," Nemenman says. "I expect to find a pattern similar to how vision neurons fire as a fly moves through the world and the scenery changes."

Story Source:

The above story is based on materials provided by Emory Health Sciences. The original article was written by Carol Clark. Note: Materials may be edited for content and length.

More From ScienceDaily

More Computers & Math News

Featured Research

Mar. 3, 2015 — By examining the forces that the segments of mosquito legs generate against a water surface, researchers have unraveled the mechanical logic that allows the mosquitoes to walk on water, which may ... full story

Mar. 3, 2015 — Major cities in the UK are falling behind their international counterparts in terms of their use of smart technologies, according to a new study. The research has found that smart cities in the UK, ... full story

Mar. 3, 2015 — To simulate chimp behavior, scientists created a computer model based on equations normally used to describe the movement of atoms and molecules in a confined space. An interdisciplinary research ... full story

Mar. 3, 2015 — Magnetic vortex structures, so-called skyrmions, could in future store and process information very efficiently. They could also be the basis for high-frequency components. For the first time, a team ... full story

Mar. 2, 2015 — The odds of picking a perfect bracket for the NCAA men's basketball March Madness championship tournament are a staggering less than one in 9.2 quintillion (that's 9,223,372,036,854,775,808), ... full story

Mar. 2, 2015 — Scientists report that they could observe experimentally the current flow along channels at the crystal surfaces of topological insulators. The channels are less than one nanometer wide and extend ... full story

Mar. 2, 2015 — Organic light emitting diodes (OLEDs), which are made from carbon-containing materials, have the potential to revolutionize future display technologies, making low-power displays so thin they'll wrap ... full story

Mar. 2, 2015 — What if one day, your computer, TV or smart phone could process data with light waves instead of an electrical current, making those devices faster, cheaper and more sustainable through less heat and ... full story

Mar. 2, 2015 — 3-D printing could become a powerful tool in customizing interventional radiology treatments to individual patient needs, with clinicians having the ability to construct devices to a specific size ... full story

Featured Videos

Forensic Holodeck Creates 3D Crime Scenes

Reuters - Innovations Video Online (Mar. 3, 2015) — A holodeck is no longer the preserve of TV sci-fi classic Star Trek, thanks to researchers from the Institute of Forensic Medicine Zurich, who have created what they say is the first system in the world to visualise the 3D data of forensic scans. Jim Drury saw it in operation.
Video provided by Reuters

Feb. 9, 2015 — New research has uncovered additional second laws of thermodynamics which complement the ordinary second law of thermodynamics, one of the most fundamental laws of nature. These new second laws are ... full story

June 20, 2012 — Neurons come in an astounding assortment of shapes and sizes, forming a thick inter-connected jungle of cells. Now, neuroscientists have found that there is a simple pattern that describes the ... full story

Apr. 16, 2012 — Could computers ever beat the best 'go' players? Although unthinkable at this stage, this could soon become possible, thanks to theorists. For the first time, scientists have applied ... full story

July 20, 2011 — A violation of one of the oldest empirical laws of physics has been observed by scientists. The experiments on purple bronze, a metal with unique one-dimensional electronic properties, indicate that ... full story

ScienceDaily features breaking news and videos about the latest discoveries in health, technology, the environment, and more -- from major news services and leading universities, scientific journals, and research organizations.